Question

Two forest fire stations, P and Q, are 20.0 km apart. A

ranger at station Q sees a fire 15.0 km away. If the angle

between the line PQ and the line from P to the fire is

how far, to the nearest tenth of a kilometre, is

station P from the fire?

Answer 1

Given that the angle is 25 degrees, we shall apply cosine rule to solve this question.
c^2=a^2+b^2-2abcosC
thus plugging the values we get:
15^2=x^2+20x^2-40xcos25
x^2-36.252x+175=0
thus solving the quadratic using quadratic formula we obtain:
x=[36.252+/-√614.208]/2
x=5.7 km or 30.5 km